- AutorIn
- Martin Kell
- Titel
- On curvature conditions using Wasserstein spaces
- Untertitel
- With an application to the q-Laplace heat equation
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:15-qucosa-149614
- Datum der Einreichung
- 17.02.2014
- Datum der Verteidigung
- 22.07.2014
- Abstract (EN)
- This thesis is twofold. In the first part, a proof of the interpolation inequality along geodesics in p-Wasserstein spaces is given and a new curvature condition on abstract metric measure spaces is defined. In the second part of the thesis a proof of the identification of the q-heat equation with the gradient flow of the Renyi (3-p)-Renyi entropy functional in the p-Wasserstein space is given. For that, a further study of the q-heat flow is presented including a condition for its mass preservation.
- Freie Schlagwörter (DE)
- Wassersteinräume, verallgemeinter Ricci-Krümmung, q-Wärmefluss, Renyi-Entropie
- Freie Schlagwörter (EN)
- Wasserstein spaces, generalized Ricci curvature, q-heat flow, Renyi entropy
- Klassifikation (DDC)
- 500
- GutachterIn
- Professor Jürgen Jost
- Professor Luigi Ambrosio
- BetreuerIn
- Professor Jürgen Jost
- Den akademischen Grad verleihende / prüfende Institution
- Universität Leipzig, Leipzig
- URN Qucosa
- urn:nbn:de:bsz:15-qucosa-149614
- Veröffentlichungsdatum Qucosa
- 05.08.2014
- Dokumenttyp
- Dissertation
- Sprache des Dokumentes
- Englisch